Method for predicting and simulating macrosegregation of directional solidification large cast ingot

Abstract

The invention discloses a macrosegregation prediction simulation method for directional solidification of a large ingot. The method specifically comprises the following steps: (1) obtaining thermophysical parameters of a material; (2) establishing a three-dimensional model of directional solidification and large cast ingots and carrying out grid division; (3) calculating mass, momentum, energy and solute transfer required by solidification of the metal material through a four-phase coupling model, wherein four phases comprise a liquid phase, an equiaxed crystal phase, a columnar crystal phase and a gas phase; (4) setting boundary conditions; (5) dynamically judging the growth areas of the isometric crystal and the columnar crystal based on the temperature gradient and the supercooling degree threshold value, wherein the columnar crystal only starts to grow from the casting mold wall and tracks the tip position of the columnar crystal; (6) iteratively solving the conservation equation of each phase until convergence, and outputting a liquid phase fraction, grain distribution and a solute concentration field; and (7) verifying by adopting an actually produced cast ingot, and quantifying the macrosegregation degree through a segregation index (SI).

Description

Technical Field

[0001] The present invention relates to a prediction and simulation method for segregation, in particular to a prediction and simulation method for macroscopic segregation of a directional solidification large ingot. Background Art

[0002] Due to the inherent solute redistribution property of alloys, liquid metals can experience solute enrichment in one phase during solidification due to the difference in chemical potential between the solid and liquid phases. This leads to segregation in the alloy. Alloy segregation can be categorized into two types: microsegregation and macrosegregation. Macrosegregation refers to uneven chemical composition within the casting size range, which is difficult to eliminate through subsequent heat treatment and severely impacts the mechanical properties of the casting. Its formation is related not only to the material composition but also to the relative flow between the solid and liquid phases. This relative flow is generally caused by multiple factors, including thermal buoyancy, solute buoyancy, and the movement of grains or inclusions. Macrosegregation exhibits a significant size effect, meaning that the larger the ingot, the more severe the macrosegregation. Accurately and efficiently predicting macrosegregation in large ingots has been a major research priority for researchers worldwide.

[0003] Directional solidification technology is a production method for manufacturing thick plates. This technology is characterized by enhancing heat dissipation from the bottom of the ingot and limiting heat dissipation in other directions, resulting in a straight solidification front and a mostly unidirectional columnar macrostructure. Because this method prevents equiaxed crystals from depositing at the bottom of the ingot, negative segregation in the ingot is completely eliminated, while positive segregation is concentrated in the last solidified area of ​​the ingot, accounting for only 8% to 11% of the ingot's height. Currently, among the simulation methods for predicting segregation in ingots, there is limited research on the macrosegregation of large ingots manufactured using directional solidification technology. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and provide a method for predicting and simulating the macrosegregation of large directional solidified ingots, so as to solve the problem that the macrosegregation is difficult to predict in the process of manufacturing large ingots by directional solidification in actual production.

[0005] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0006] A method for predicting and simulating macrosegregation of a large directional solidification ingot comprises the following steps:

[0007] (1) Obtaining the thermal physical properties of the material;

[0008] (2) Establish three-dimensional models of directional solidification and large ingots and perform meshing;

[0009] (3) Calculate the mass, momentum, energy, and solute transport required for solidification of metal materials using a four-phase coupling model, where the four phases include liquid, equiaxed, columnar, and gas phases;

[0010] (4) Set boundary conditions:

[0011] The contact surface temperature of the water-cooled copper plate at the bottom is kept constant at 300-450℃;

[0012] The refractory brick shell adopts a convection heat transfer model with a heat transfer coefficient of 30-70W / (m 2 K);

[0013] The thermal conductivity of the top carbonized rice husk layer was set to 5-10 W / (m·K);

[0014] (5) Dynamically determine the growth areas of equiaxed crystals and columnar crystals based on the temperature gradient and undercooling threshold. Columnar crystals only grow from the mold wall and their tip positions are tracked.

[0015] (6) Iteratively solve the conservation equations of each phase until convergence, and output the liquid phase fraction, grain distribution, and solute concentration field;

[0016] (7) The actual ingots produced were used for verification, and the degree of macrosegregation was quantified by the segregation index (SI).

[0017] A further preferred embodiment of the present invention is that: in the four-phase coupling model in (3), the mass is calculated using the mass conservation equation, the momentum is calculated using the momentum conservation equation, the energy conservation equation is calculated using the energy conservation equation, and the solute transport is calculated using the composition conservation equation; specifically:

[0018] The mass conservation formula is:

[0019]

[0020] Momentum conservation formula

[0021]

[0022] Conservation of composition formula:

[0023]

[0024] 4) Energy conservation formula

[0025]

[0026] in:

[0027] A further preferred embodiment of the present invention is that: the equiaxed crystal growth rate in (5) is:

[0028]

[0029] Equiaxed solidification rate:

[0030]

[0031] A further preferred embodiment of the present invention is that the growth rate of the main columnar crystal in (5) is:

[0032]

[0033] σ c =d c / 10

[0034] Solidification rate of columnar crystal trunk:

[0035]

[0036] Solidification rate at the tip of columnar crystal:

[0037]

[0038] where Φ imp refers to the growth front collision parameter, λ1 is the primary dendrite arm spacing, and λ1 = 0.000129 m;

[0039]

[0040] A further preferred embodiment of the present invention is that: in (7), the degree of macrosegregation is quantified by the segregation index (SI):

[0041]

[0042] Among them, C max 、C min are the maximum and minimum concentrations of solute in the ingot, respectively, and C0 is the initial concentration.

[0043] The beneficial effects of the present invention are:

[0044] (1) The present invention adopts a four-phase model to predict the macrosegregation phenomenon during the directional solidification of large ingots by coupling and solving the mass, momentum, energy and solute transport equations between the metal liquid phase, equiaxed crystal phase, columnar crystal phase and gas phase during the directional solidification of large ingots;

[0045] (2) The present invention provides a simplified method for boundary conditions and initial conditions of the directional solidification process of large ingots, simplifies the macrosegregation simulation of the directional solidification process of large ingots, and improves the calculation efficiency;

[0046] (3) The present invention provides parameter settings for the drag force coefficients between equiaxed crystals, columnar crystals, and liquid phases, providing a reference for the simulation of macrosegregation during the directional solidification process of large ingots under specific conditions;

[0047] (4) The present invention is applicable to predicting the macro-composition distribution of ingots of various materials and large tonnage, and serves as a reference for optimizing the directional solidification casting process. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 The curve of the surface temperature of the water-cooled copper plate changing with time is drawn through numerical simulation;

[0049] Figure 2 It is a schematic diagram of the 45-ton ingot casting and directional solidification device;

[0050] Figure 3 is the setting of thermal boundary conditions used in the simulation process;

[0051] Figure 4 It is the liquid phase distribution diagram at 1000s;

[0052] Figure 5 It is the liquid phase distribution diagram at 3000s;

[0053] Figure 6 It is the liquid phase distribution diagram at 7000s;

[0054] Figure 7 This is a schematic diagram of the volume distribution cloud of the liquid-solid interface, equiaxed crystals, and columnar crystals during the solidification process of a 45-ton ingot.

[0055] Figure 8 It is the distribution diagram of segregation index of the center line and the straight lines with different x-coordinate values ​​from the coordinate origin;

[0056] Figure 9 This is the macro segregation distribution cloud of C element in 45-ton ingot;

[0057] In the figure, 1 is carbonized rice husk; 2 is ingot; 3 is refractory wall shell; 4 is water-cooled copper plate. DETAILED DESCRIPTION

[0058] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific implementation methods.

[0059] Example 1

[0060] This embodiment provides a method for predicting and simulating macrosegregation of a large directional solidification ingot, which specifically includes the following steps:

[0061] (1) Obtaining the thermal physical properties of the material;

[0062] (2) Establish three-dimensional models of directional solidification and large ingots and perform meshing;

[0063] (3) calculating the mass, momentum, energy, and solute transport required for solidification of the metal material using a four-phase coupling model;

[0064] (4) setting equation solving convergence characterization parameters, boundary conditions, and calculation methods, and coupling solving the mass, momentum, energy, and solute transfer between the liquid phase, the solid phase in the equiaxed crystal, and the columnar crystal phase of the metal material;

[0065] (5) Before starting the iterative calculation, set the initial calculation conditions and initialize the wall to determine the starting point of columnar crystal growth;

[0066] (6) Start iterative calculation, calculate the temperature gradient of each unit, and determine the growth area of ​​columnar crystals and equiaxed crystals;

[0067] (7) Through the phase coupling algorithm in Fluent, the transport equations of mass, momentum, energy, and solute of each phase are solved in a coupled manner;

[0068] (8) Tracking the solid-liquid surface and the plane where the columnar crystal growth tip is located;

[0069] (9) Determine whether the convergence condition is met. If the condition is not met, repeat the iteration from step (6). If the condition is met, proceed to the next time step calculation until the simulation result is obtained.

[0070] (10) After the calculation is completed, analyze the calculation results;

[0071] (11) Use the directional solidification device to actually produce ingots and record the actual production results;

[0072] (12) Comparing the simulation results with the actual production results to verify the reliability of the simulation results, and making further improvements, and then using them for prediction of subsequent large ingots.

[0073] The boundary conditions set above are specifically:

[0074] According to the temperature field simulation results of the directional solidification heat sink-water-cooled copper plate, as shown in Figure 1 The copper plate temperature and the runner water temperature both reach their maximum temperature at 10 seconds, then slowly decrease to 400°C as their final steady-state temperature. This temperature is set as the first type of thermal boundary condition when the molten metal is in direct contact with the water-cooled copper plate. That is, from the beginning of mold filling to the completion of solidification, the bottom water-cooled copper plate and the contact surface between the molten metal and the ingot are kept at a constant 400°C.

[0075] The heat exchange between the refractory shell of the directional solidification device and the external environment is set to convection heat exchange, the external air temperature is set to 300℃, and the convection heat transfer coefficient is 50W / (m 2 k), the thermal conductivity of the refractory brick shell is set to 0.137W / (m 2 k);

[0076] Considering that the refractory shell of the top of the directional solidification device is open and covered with carbonized rice husks in the actual production process, this part is simplified to a material with a height of 60 mm in the simulation, and its thermal conductivity is set to 8 W / (m 2 k), with the external convection heat exchange set up in the same manner as in (2);

[0077] In the above four-phase coupling model, the mass conservation equation is used to calculate the mass, the momentum conservation equation is used to calculate the momentum, the energy conservation equation is used to calculate the energy, and the composition conservation equation is used to calculate the solute transport; specifically:

[0078] The mass conservation formula is:

[0079]

[0080] Momentum conservation formula

[0081]

[0082]

[0083] Conservation of composition formula:

[0084]

[0085] Energy conservation formula

[0086]

[0087] in:

[0088]

[0089] Determination of the above growth conditions for equiaxed crystals and columnar crystals:

[0090] As long as the corresponding undercooling exists, equiaxed crystals are allowed to nucleate and grow in all units; while columnar crystals only start to grow from the mold wall. The temperature gradient of each unit is then tracked to determine the growth direction of the columnar product. At the same time, when the temperature gradient of the unit meets a threshold and the amount of equiaxed crystals deposited at the front of the columnar crystal is less than a certain amount, the columnar crystal can grow in the opposite direction of the heat flow.

[0091] The equiaxed crystal growth rate is:

[0092]

[0093] Equiaxed solidification rate:

[0094]

[0095] The growth rate of the columnar crystal trunk is:

[0096]

[0097] σ c =d c / 10

[0098] Solidification rate of columnar crystal trunk:

[0099]

[0100] Solidification rate at the tip of columnar crystal:

[0101]

[0102] where Φ imp refers to the growth front collision parameter, λ1 is the primary dendrite arm spacing, and λ1 = 0.000129 m;

[0103]

[0104] Compute the source and exchange terms and adjust the drag force coefficient:

[0105] 1) Momentum transfer:

[0106]

[0107] in is the momentum transfer K between the liquid phase and the equiaxed crystal caused by the drag force le is the drag coefficient between the liquid phase and the equiaxed crystal phase.

[0108]

[0109] i=0.176log 10 (β d )+0.275;

[0110] Where: Φ e is the shape factor Φ e =0.28;

[0111] f si is the solid phase ratio f inside the equiaxed crystal envelope si =f s / f env f s =0.6; f env=0.637;

[0112]

[0113] in is the momentum transfer between the liquid phase and columnar crystals due to the drag force

[0114] in

[0115] Mass Transfer:

[0116]

[0117] Heat Transfer:

[0118]

[0119] Update thermophysical property parameters and judge convergence:

[0120] Unit average solute tracking calculation:

[0121]

[0122] The degree of macrosegregation is quantified by the Segregation Index (SI):

[0123]

[0124] Among them, C max 、C min are the maximum and minimum concentrations of solute in the ingot, respectively, and C0 is the initial concentration.

[0125] In addition to the above embodiments, the present invention may also have other implementation methods; any technical solutions formed by equivalent replacement or equivalent transformation fall within the protection scope required by the present invention.

Claims

1. A method for predicting and simulating macrosegregation in directional solidification large ingots, characterized by: The specific steps include: (1) Obtaining the thermal physical properties of the material; (2) Establish three-dimensional models of directional solidification and large ingots and perform meshing; (3) Calculate the mass, momentum, energy, and solute transport required for solidification of metal materials using a four-phase coupling model, where the four phases include liquid, equiaxed, columnar, and gas phases; (4) Set boundary conditions: The contact surface temperature of the water-cooled copper plate at the bottom is kept constant at 300-450℃; The refractory brick shell adopts a convection heat transfer model with a heat transfer coefficient of 30-70W / (m 2 K); The thermal conductivity of the top carbonized rice husk layer was set to 5-10 W / (m·K); (5) Dynamically determine the growth areas of equiaxed crystals and columnar crystals based on the temperature gradient and undercooling threshold. Columnar crystals only grow from the mold wall and their tip positions are tracked. (6) Iteratively solve the conservation equations of each phase until convergence, and output the liquid phase fraction, grain distribution, and solute concentration field; (7) The actual ingots produced were used for verification, and the degree of macrosegregation was quantified by the segregation index (SI).

2. The method for predicting and simulating macrosegregation of a directional solidification large ingot according to claim 1, wherein: In the four-phase coupling model (3), the mass conservation equation is used to calculate the mass, the momentum conservation equation is used to calculate the momentum, the energy conservation equation is used to calculate the energy, and the composition conservation equation is used to calculate the solute transport; specifically: The mass conservation formula is: Momentum conservation formula Conservation of composition formula: 4) Energy conservation formula in:

3. The method for predicting and simulating macrosegregation of a directional solidification large ingot according to claim 1, wherein: The equiaxed crystal growth rate in (5) is: Equiaxed solidification rate:

4. The method for predicting and simulating macrosegregation of a directional solidification large ingot according to claim 3, wherein: The growth rate of the main columnar crystal in (5) is: s c =d c / 10 Solidification rate of columnar crystal trunk: Solidification rate at the tip of columnar crystal: where Φ imp refers to the growth front collision parameter, λ1 is the primary dendrite arm spacing, and λ1 = 0.000129 m; 5. The method for predicting and simulating macrosegregation of a directional solidification large ingot according to claim 1, wherein: The degree of macrosegregation is quantified by the segregation index (SI) in (7): Among them, C max 、C min are the maximum and minimum concentrations of solute in the ingot, respectively, and C0 is the initial concentration.

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